Abstract. We consider the problem of data propagation in wireless sensor networks and revisit the family of mixed strategy routing schemes. We show that maximizing the lifespan, balancing the energy among individual sensors and maximizing the message flow in the network are equivalent. We propose a distributed and adaptive data propagation algorithm for balancing the energy among sensors in the network. The mixed routing algorithm we propose allows each sensor node to either send a message to one of its immediate neighbors, or to send it directly to the base station, the decision being based on a potential function depending on its remaining energy. By considering a simple model of the network and using a linear programming description of the message flow, we prove the strong result that an energy-balanced mixed strategy beats every other possible routing strategy in terms of lifespan maximization. Moreover, we provide sufficient conditions for ensuring the dynamic stability of the algorithm. The algorithm is inspired by the gradient-based routing scheme but by allowing to send messages directly to the base station we improve considerably the lifespan of the network. As a matter of fact, we show experimentally that our algorithm is close to optimal and that it even beats the best centralized multi-hop routing strategy.

We propose an algorithm which produces a randomized strategy reaching optimal data propagation in wireless sensor networks (WSN). In [6] and [8], an energy balanced solution is sought using an approximation algorithm. Our algorithm improves by (a) when an energy-balanced solution does not exist, it still finds an optimal solution (whereas previous algorithms did not consider this case and provide no useful solution) (b) instead of being an approximation algorithm, it finds the exact solution in one pass. We also provide a rigorous proof of the optimality of our solution.

Geographic routing scales well in sensor networks, mainly due to its stateless nature. Still, most of the algorithms are concerned with finding some path, while the optimality of the path is difficult to achieve. In this paper we are presenting a novel geographic routing algorithm with obstacle avoidance properties. It aims at finding the optimal path from a source to a destination when some areas of the network are unavailable for routing due to low local density or obstacle presence. It locally and gradually with time (but, as we show, quite fast) evaluates and updates the suitability of the previously used paths and ignores non optimal paths for further routing. By means of extensive simulations, we are comparing its performance to existing state of the art protocols, showing that it performs much better in terms of path length thus minimizing latency, space, overall traffic and energy consumption.

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Abstract.A wide range of applications in wireless sensor networks rely on the location information of the sensing nodes. However, traditional localization techniques are dependent on hardware that is sometimes unavailable (e.g. GPS), or on sophisticated virtual localization calculus which have a costly overhead.Instead of actually localizing nodes in the physical two-dimensional Euclidean space, we use directly the raw distance to a set of anchors to produce multi-dimensional coordinates. We prove that the image of the physical two-dimensional Euclidean space is a two-dimensional surface, and we show that it is possible to adapt geographic routing strategies on this surface, simply, efficiently and successfully.

Abstract. We show how a lattice Boltzmann (LB) scheme can be spatially coupled with a finite difference (FD) scheme in order to solve the same problem. The typical situation we consider is a computational domain which is partitioned in two regions. The same spatio-temporal physical process extends over the full domain but a different numerical method is used over each region. At the interface of the subdomains, the LB and FD must be connected so as to ensure a perfect continuity of the physical quantities. We derive the theoretical concepts, which allow us to link both methods in the case of a diffusion process, and validate them with numerical simulations on a 2D domain.

Abstract-In this paper, we propose an efficient planarization algorithm and a routing algorithm dedicated to Unit Disk Graphs whose nodes are localized using the Virtual Raw Anchor Coordinate system (VRAC). Our first algorithm computes a planar 2-spanner under light constraints on the edge lengths and induces a total exchange of at most 6n node identifiers. Its total computational complexity is O(n∆), with ∆ the maximum degree of the communication graph. The second algorithm that we present is a simple and efficient algorithm to route messages in this planar graph that requires routing tables with only three entries. We support these theoretical results by simulations showing the robustness of our algorithms when the coordinates are inaccurate.

Abstract. This paper studies the data gathering problem in wireless networks, where data generated at the nodes has to be collected at a single sink. We investigate the relationship between routing optimality and fair resource management. In particular, we prove that for energy balanced data propagation, Pareto optimal routing and flow maximization are equivalent, and also prove that flow maximization is equivalent to maximizing the network lifetime. We algebraically characterize the network structures in which energy balanced data flows are maximal. Moreover, we algebraically characterize communication links which are not used by an optimal flow. This leads to the characterization of minimal network structures supporting the maximal flows. We note that energy balance, although implying global optimality, is a local property that can be computed efficiently and in a distributed manner. We suggest online distributed algorithms for energy balance in different optimal network structures and numerically show their stability in particular setting. We remark that although the results obtained in this paper have a direct consequence in energy saving for wireless networks they do not limit themselves to this type of networks neither to energy as a resource. As a matter of fact, the results are much more general and can be used for any type of network and different types of resources. 3